After Babbage began work on the Analytical Engine in late 1834, he largely ignored the further development of the Difference Engine for over a decade, although he was still negotiating with the government as to the status of the project for its construction through 1842, as described in Chapter Two. Only occasionally did material on mechanisms for the Difference Engine or on ways to do finite difference calculations on the Analytical Engine appear in Babbage's notebooks. ² However, in October, 1846, Babbage abruptly turned his attention back to the Difference Engine, or rather what he called the New Difference Engine, ³ and later the Difference Engine No. 2, and away from the Analytical Engine.

Exactly why this great change in interest occurred is not clear. Writing in 1864 in Passages from the Life of a Philosopher, Babbage said that he turned his attention to the Difference Engine No. 2 "when I had mastered the subject of the Analytical Engine." ⁴ However, considerably closer to the event, in his book The Exposition of 1851, ⁵ Babbage gave a rather different account. He said that after the invention of the Analytical Engine, "I instituted a long series of experiments for the purpose of reducing the expense of its construction to limits which might be within the means I could myself afford to supply. I am now resigned to the necessity of abstaining from its construction, and feel indisposed even to finish the drawings of one of its many general plans." It is indeed plausible that Babbage had to an extent simply gotten tired of working on the Analytical Engine; although he was still turning out a fairly large number of Notations, the number of Drawings and the amount of space in the Scribbling Books taken up with the Analytical Engine had declined greatly from a few years earlier.

However, there was one other circumstance which may have caused Babbage to return to the consideration of the design of a Difference Engine at this time, although he gave no hint of it in any of his writings. In July, 1846, the Conservative government headed by Sir Robert Peel, who had finally terminated official support for the first Difference Engine, and who refused to admit that any gratitude or honor was due Babbage for his labors on it, was replaced by a Whig government with Lord John Russell as Prime Minister.

Babbage apparently thought that an appeal to the new government might produce some redress of the injustice he felt he had suffered from the old one, and he correspondingly wrote a long letter to the Prime Minister in December, 1845, describing the many contributions he had made to science and art, and the many positions which had been refused to him despite his high qualifications. ⁶

Once again, as with Babbage's letters to the government in the 1830s, it is not clear what result he was attempting to produce. In very vague terms, Babbage simply appealed to Russell "against the injustice of the past. It is for you as the first minister of the crown to adopt or repair it." ⁷ How Russell could or should repair it Babbage did not suggest, and he also did not mention his efforts of the previous two-months to design "a Difference Engine of the simplest construction." ⁸ But that Babbage had in mind some scheme for getting the government to acknowledge the unjust neglect with which it had treated him, and then proposing that they undertake to construct the new Difference Engine, seems fairly clear,

In any case, Babbage did not send his letter to the Prime Minister, although at some point after June, 1847 (possibly as much as two or three years after), ⁹ he extensively revised and shortened it, again apparently without sending it. Another letter, probably some later version of this same one, was prepared in December 1849, and sent to the Earl of Rosse, President of the Royal Society, for suggestions, but it is again unclear whether this letter was sent to Lord Russell. ¹⁰

In the meantime, Babbage had been working on the design of the Difference Engine No. 2, and by March, 1848, he had prepared a complete set of drawings and notations, ¹¹ although some additional work was done through March, 1849. ¹² However, on February 16, l849, Babbage had written to a friend with respect to the Engine:

I am now winding up that affair; ill health and other circumstances have brought on a crisis, and I shall avail myself of it to close the account, I hope forever.

I agree with you entirely as to the magnitude of the debt this country owes to science, but I probably differ from you in disbelieving the capacity of the present race of statesmen either to feel or to repay it. ¹³

Work on the Difference Engine ceased in March, 1849. For a short time thereafter Babbage returned to a consideration of the Analytical Engine, but this was quite sporadic, and it ended on May 7, 1849. ¹⁴ After this there was no further work on any calculating machine plans until 1857. Already in March, Babbage had been attempting to find some other position for C. G. Jarvis, who had been working on the designs for Babbage's machines ever since the first Difference Engine; ¹⁵ whether he succeeded is not clear.

Babbage wrote no general description of the Difference Engine No. 2, or of how it differed from Difference Engine No. 1, although he claimed that it was "an instrument of greater power as well as of greater simplicity than that formerly commenced." ¹⁶ However, from the drawings it appears that it was basically very similar in general design to the earlier machine. Digits were to be added from one difference to that above it by raising and lowering the various axes, as in the Analytical Engine, rather than by the somewhat clumsy method of bolting used earlier; but the basic principle of adding the odd and even differences in two groups was the same, and the method of carriage, on which Babbage had spent so much of his effort on the Analytical Engine, was basically the same as that used on the first Difference Engine. The main change from both earlier machines was that for the Difference Engine No. 2, Babbage had a complete set of plans for the whole machine, including the printing apparatus; Babbage was able to formulate one basic design for the whole machine and then draw all of the component parts consistent with it, as opposed to the invariable experimental altering of what was already designed characteristic of the plans for the Analytical Engine. Apparently the new Difference Engine was to have seven orders of differences, each column able to hold thirty digits. The whole machine would have been over ten feet long, but this was partly because the driving, calculating and printing sections were all strung out in a line. Despite Babbage's statement that the new Difference Engine would have "greater power" than the old, there is no indication that he planned to incorporate any mechanism for making the machine "eat its own tail."

Such, very briefly, was the character of the new Difference Engine. Two circumstances led Babbage to believe that an attempt to construct it would be more successful and less expensive than that to build the first Difference Engine. First, Babbage felt that he had been quite successful in "simplifying and expediting the mechanical processes" of the Difference Engine No. 1. ¹⁷ Second:

circumstances had changed, mechanical engineering had made much progress, the tools required and trained workmen were to be found in the workshops of the leading machinists, the founder's art was so advanced that casting had been substituted for cutting in making the change wheels even of screw-cutting engines, and therefore it was very probable that persons would be found willing to undertake to complete the Difference Engine for a specific sum. ¹⁸

As mentioned above, Babbage had sent to Lord Rosse, President of the Royal .Society, a draft of a letter to Lord Russell, Prime Minister, in December, 1849, many months after Babbage had completed working on the plans of the new machine. But whether this letter contained an offer of the plans to the government is not clear; in any case it appears that the letter was not sent. For some reason the matter rested until the spring of 1852, at which point the government headed by Lord Derby replaced that of Lord John Russell. At that point, Babbage decided that he would get Lord Rosse to present to Lord Derby an offer of the plans for the new machine, in order "that I may fulfill to the utmost of my power the original expectation that I should be able to complete, for the Government, an Engine capable of calculating astronomical and nautical Tables with perfect accuracy." ¹⁹ Yet Babbage was not willing to devote his own time to building the new Difference Engines only to make the plans available. ²⁰ On the other hand, he would not propose that the government construct the Analytical Engine, since:

it is not so matured as to enable any other person, without long previous training and application, even to attempt its execution; and on my own part, to superintend its construction would demand an amount of labour, anxiety and time which could not, after the treatment I have received, be expected of me. ²¹

Babbage was not optimistic about the prospects of this offer. Replying to a letter from Rosse dated July 22, 1852, ²⁶ informing him that Rosse had presented the case to Derby, Babbage said that with respect to the likelihood of having the calculating machines constructed:

I have never entertained much hope, and I now feel a kind of relief at being no longer obliged to think on a painful subject.

I have been trying to exclude the idea by the enquiry into the great law of matter, but I am obliged for a time to vary my occupation, and am now busied with the Automaton player at Tit-Tat-To.

Perhaps if I were to make that toy, my countrymen right think there was some merit in the Analytical Engine. ²⁷

The Prime Minister responded to the offer of the plans for the Difference Engine No. 2 on August 16, 1852. On that date, W.P. Talbot, secretary to Lord Derby, wrote to Rosse informing him that Derby had taken the documents sent him by Rosse under consideration, and had consulted with the Chancellor of the Exchequer (Benjamin Disraeli); his conclusion was:

that Mr. Babbage's projects appear to be so indefinitely expensive, the ultimate success so problematical, and the expenditure certainly so large and so utterly incapable of being calculated, that the Government would not be justified in taking upon itself any further liability. ³¹

Curiously, Babbage somewhat misread the letter from Talbot, thinking that it attributed to Disraeli opinions said to come from Derby, and this mistake persisted through the account of the offer of the second Difference Engine given in Passages from the Life of a Philosopher in 1864. There Babbage blamed the whole matter on the Chancellor of the Exchequer, saying, for example, that "the machine upon which everybody could calculate had little chance of fair play from the man upon whom nobody could calculate;" ³⁴ and that: "It can not only calculate the millions the ex-Chancellor of the Exchequer squandered, but it can deal with the smallest quantities. . . It may possibly enable him to un-muddle even his own financial accounts." ³⁵ And Babbage concluded, "The Herostratus of Science, if he escape oblivion, will be linked with the destroyer of the Ephesian Temple." ³⁶

Rosse replied to Babbage's letter of August 27 on the 29th. ³⁷ He pointed out that most of the points Babbage had made had already been expressed in the letter he had sent to Derby himself, accompanying Babbage's offer of the-plans. He also quoted two of the most important of these remarks, ones which he made on the basis of a statement he had elicited from the distinguished engineer James Nasmyth. ³⁸ As Rosse had expressed it to Derby:

From what I have heard from eminent mechanical engineers, there is no doubt that this Country has received an equivalent many times over for the expenditure on the Calculating engine, in the improvements in tools and machinery directly traceable to the attempt to make it. . . .

Tools and machinery are now in so advanced a state compared to what they were when the machine was commenced that it is probable some mechanical engineer would be found to undertake the work by contract. ³⁹

In a speech to the Royal Society, as President, in 1855, Rosse gave an account of the history of the Babbage Difference Engine, and repeated the assertion that "the expense of the Calculating Engine had been more than repaid in the improvements in mechanism directly referable to it." ⁴⁰ It apparently occurred to 8abbage after this address that he might get wide agreement on this point among engineers. He therefore wrote to three of the most distinguished engineers of the day, Joseph Whitworth, William Fairbairn and James Nasmyth, asking then to confirm Rosse's statement. ⁴¹ Whitworth's reply is not to be found, but from a further letter Babbage wrote to him it is evident that he misunderstood Babbage's request, for he offered to make a contribution toward the cost of constructing the Analytical Engine; this Babbage declined. ⁴² Fairbairn sent an elaborate formal statement, which concluded that "the labours of Mr. Babbage in devising and constructing the Calculating Machine have led to the most important results . . in the general improvements referable to mechanical construction." ⁴³

The most elaborate praise was contained in the letter from Nasmyth, which also gives a nice indication of the high regard in which the mechanical arts were widely held at the time. Writing to Babbage on June 22, 1855, Nasmyth said:

I have no hesitation in stating that whatever were the direct results of your endeavour to carry out into a practical form your idea of a "Calculating machine," the indirect Results were most valuable to mankind in as much as that the admirable contrivances and tools which the late Mr. Joseph Clement in conjunction with yourself designed and constructed (for Executing with due perfection the Exquisite apparatus required to realize your great object) furnished such ideas to the mechanists of the world as gave an impulse towards the perfect in mechanism, such as has had no small share in bringing about the wonders which modern machinery has enabled us to realize.

Beginning with the admirable and ever to be remembered contrivances of Sir Samuel Bentham, who I hold to be the true originator of modern Engineering Tools, and taking next in order Henry Maudsley of glorious memory, we come to Joseph Clement and your worthy self, who in your joint endeavours to realize your ideas of a Calculating machine gave I may say the finishing touches to those mechanical agencies by the aid of which we are now almost getting the mastery over Time, Space and the matter of our globe, which I am fain to consider one of the grandest objects of human existence as a powerful means towards "the greatest happiness to the greatest number." ⁴⁴

I have heard at different times from men I had employed in former years that amongst their own class it was frequently said that:

Mr. Babbage made Clement.
Clement made Whitworth.
Whitworth made the tools.

When I first employed Clement he possessed one lathe (a very good one) and his workshop was in a small front kitchen.

When I ceased to employ him he valued his tools at several thousand pounds and he had converted a large chapel into workshops. ⁴⁶

Aside from these inventions, Clement's other greatest contribution to machinery, also developed while working for Babbage, was uniform threads for taps and dies. Previously, the number of threads had been made largely at random, so that different screws were generally incompatible; in 1827 Clement began making his taps with a certain integral number of threads to the inch, depending on the diameter, so that different screws would be interchangeable. This practice was learned by Joseph Whitworth (1803-1887), who worked for Clement between 1831 and 1833; Whitworth was later able to get the thread specifications, which he further improved, adopted as a uniform standard through most of the world. ⁴⁹

One thing that is more difficult to judge is what proportion of the work of Clement's shop was devoted to Babbage's machine. Smiles does not make this clear, although he states that Clement's "principal income" came from work done on his planing machine (the only one at the time capable of handling really large work), and that Clement at times employed as many as thirty assistants; ⁵⁰ this implies that work for Babbage was a relatively small part of Clement's business. However, although Smiles states that the planing machine was built in 1825, ⁵¹ Clement's nephew (who took over Clement's shop on his death in 1844 ⁵² ) stated in reply to an enquiry from Babbage in 1855 that the planing machine was finished in 1831; ⁵³ it thus could not have been Clement's principal source of income before then. Further, the fact that in 1832 Clement was willing to consider moving to the special workshop being built for the Difference Engine ⁵⁴ strongly suggests that work on it was not a minor part of his business. Still, it is clear that by 1832 Clement's business was prosperous, and that he could afford to lose the Difference Engine work; but this is fully compatible with Babbage's statement, quoted above, that "Mr. Babbage made Clement."

Returning to the remarks made by Rosse to Derby in 1852, only one piece of evidence will be offered in support of the assertion that improvements in machine tools would make the construction of the Difference Engine No. 2 far easier than the work on the Difference Engine No. 1. In his address as the President of the Institution of Mechanical Engineers in 1856, ⁵⁵ Joseph Whitworth discussed the improvements in manufacturing technique that had been made since 1826. To cite only one specific point, the cost of finishing a cast iron surface by hand in the earlier year had been about twelve shillings per square foots but with the planing machines of the 1850s, the same operation cost about one penny per square foot, a reduction in the cost of a very basic operation by a factor of 144. This may go a long way toward explaining the high cost of the work on the original Difference Engine.

After 1849, Babbage had ceased working on the mechanical details of any of his calculating machines, and after 1852 he also ceased for a few years to make any substantial effort at promoting their construction or use. However, during the mid 1850s, he did spend a considerable amount of time supporting the Scheutz Difference Engine and helping its builders, and an account of this work must be given, though primarily from the point of view of Babbage's role.

Per Georg Scheutz (1785-1873) attended the University of Lund and Its Law School and served a few years of employment in the law, but in 1817 he entered the field to which he was to devote most of his life; publishing and journalism. For many years he served as co-owner of a printing company, publisher of newspapers and trade journals, and translator; he also served as a reporter for his own and other papers, particularly on economic and technical subjects, and after 1842 this was his primary occupation. Georg's son Edvard (1821-1881) was born in 1821 and entered the Technological Institute in Stockholm in 1835; he was still there when work on the Scheutz Difference Engine began. ⁵⁶

In 1834, Georg Scheutz read in the Edinburgh Review the article on the Babbage Difference Engine by Dionysius Lardner, ⁵⁷ "Unfortunately for himself, Mr. Scheutz was fascinated by the subject, and impelled by an irresistible desire to construct an engine for the same purposes," as Babbage was later to express it. ⁵⁸ Scheutz made a few models of different parts of the machine out of crude materials to test his ideas, but at first carried the project no further. During the summer vacation of 1837, Edvard Scheutz, now seventeen years old, became interested in the project, and father and son together revised and extended the earlier plans to the point where they were sufficiently satisfied with them to apply, on October 30, 1837, for support from the Swedish government to construct the machine; this was refused on February 21, 1838. ⁵⁹

The plans continued to be developed and improved, until, by mid 1843, the Scheutzes had produced working models of the different sections of this machine, including the printing apparatus. This crude demonstration version of the Difference Engine was inspected by a distinguished committee from the Royal Swedish Academy of Sciences on September 18, 1843, they issued a report describing the capabilities of the machine. Georg and Edvard Scheutz hoped to use this favorable report to help solicit orders for full, finished version of the Engine, but they were not successful, and the model stood idle for many years. ⁶⁰

For some reason interest in the machine was revived in December, 1850, when a new committee from the Royal Academy of Sweden inspected it; this led the Scheutz's to apply again to the government on January 28, 1851. The government referred the matter to the Academy of Sciences, which advised that the project should be supported, but on April 29, 1831, the government decided against giving support. However, the question was raised again in the Diet, and a motion was passed proposing that the Scheutzes be given the equivalent of £280, ⁶¹ providing that the machine when complete was found to work successfully. The Scheutzes had to petition, however, to receive the money in advance; this was granted on October 24, 1851, provided they obtained guarantees that the money would be repaid if the machine was not finished satisfactorily by the end of 1853; they were able to get pledges toward repaying the money in case they should fail from various members of the Swedish Academy.

The working drawings of the machine were completed on February 1, 1852, and the machine was built at the workshop of C.W. Bergström in Stockholm, under the superintendence of Edvard Scheutz, being completed in October, 1853. The Royal Academy pronounced the machine to be satisfactory, and as a consequence of their suggestion, the Diet awarded the Scheutzes an additional £280.

At this point a few remarks will be in order as to the relation of the Scheutz Difference Engine to the Babbage Difference Engine No. 1 (from a description of which the Scheutzes had begun), though nothing will be said by way of mechanical description of the Scheutz machine. In principle, the two machines were identical; even the basic approach to the mechanical design of the various operations was quite similar, though in the Scheutz machine the printing apparatus was much more fully developed. The principle differences lay in the actual detail of the adding and carriage mechanisms; partly these arose from the fact that the Scheutz calculating section was rotated ninety degrees with respect to the Babbage calculating mechanism; that is, each successive difference was arranged horizontally across the front of the machine, with a wheel on a given level of each successive axis corresponding to each successive digit of a given order of difference; yet although this made the machine look quite different from the Babbage version, it was not in fact a significant change.

More important was that the mechanism for adding individual digits was considerably revised, in such a way that it was considerably more compact and easier to construct, but on the other hand it was also considerably more delicate and unreliable. The other main change was in the carriage mechanism; in Babbage's machine carriages had been delayed and sequential, being caused by arms set in spiral form on axes which turned at the appropriate time; this allowed second and higher order carries to be made without difficulty. On the Scheutz machine the carries were still delayed and sequential, but they were performed by a special pair of devices which slid back and forth on tracks in front and back of the machine, and which bore, as Babbage said. "a certain analogy to a railway having fifteen stations," ⁶² This carriage mechanism, though highly ingenious, was definitely less satisfactory than Babbage's; although a good deal more delicate, it was really no simpler in construction or operation. Worse, it was tremendously slower, taking about twelve to fourteen seconds for one set of carries, where the Babbage version would have taken about one second. In part this was offset by having some of the carries performed while printing was going on, but the printing mechanism was itself very slow, and even accepting it, half the carriage time was still wasted.

In short, though clever in design, the Scheutz Difference Engine was definitely inferior to the Babbage Difference Engine. It was substantially less reliable; worse, it was extremely slow; where the Scheutz machine took thirty seconds to calculate one new number, the Babbage machine could find it in about four seconds (although the provision of a printing apparatus might have slowed it down somewhat). Indeed, the only advantage of the Scheutz machine, real enough to be sure, was that it actually did get built. ⁶³

The final reward to the Scheutzes for their work mentioned above was decided on by the Swedish Diet on August 11, 1854. As it was their hope to make some profit from their invention by obtaining orders for copies of it, particularly from foreign countries, they set off with the machine for England in October, 1854, and they spent the rest of the year in England and France, though the machine stayed in England. On October 17, 1854 they applied for an English patent for the machine, and it was issued on April 13, 1855. ⁶⁴ In London, the Scheutzes were introduced to the firm of Bryan Donkin & Co., Civil Engineers, and the machine was deposited at the firm to be exhibited. There they met William Gravatt, who, together with Babbage, did the most to publicize, display and try to get sales for the Scheutz machines; through them it was deposited at the Royal Society, where it was repeatedly demonstrated by Gravatt, including among its visitors Prince Albert, on January 29, 1855.

On January 21, 1855 a special committee of the Royal Society, headed by George G. Stokes, issued a report on the Scheutz Difference Engine. It mentioned the relation of the Scheutz machine to Babbage's, and spoke approvingly of the smoothness with which the former operated, but it devoted most of its attention to the limits placed on the machine by the fact that it had only four orders of differences; this led to the conclusion that the machine would be useful primarily for recalculating old mathematical tables. ⁶⁵

In June, Babbage heard of this report from Charles Wheatstone, another member of the committee, and he wrote to Stokes saying that he was glad that they had investigated the general problem of calculating tables on difference engines, although he had "no intention under any circumstances of ever making such a machine myself." ⁶⁶ He went on to point out that the limitations discussed in the committee's report were to a degree overcome by the method he had devised for altering the last difference.

Charles' son Henry P. Babbage had been in India since 1843 in the service of the East India Company. In late 1854 he returned to England on an extended furlough. His father taught him the mechanical notation which he had invented in 1826 and subsequently developed, and on April 4, 1855, Henry was set to work using the mechanical notation to describe the operation of the Scheutz Difference Engine, which at that time was still housed at the Royal Society. ⁶⁷ He continued working on this project through the summer, and the large charts which resulted were finished in time to be used as illustrations in a talk on the mechanical notation which Henry delivered to the meeting of the British Association in Glasgow in September 1855. ⁶⁸ They were used again in a joint paper by Henry and Charles on the Scheutz machine and the mechanical notation delivered to the Institution of Civil Engineers on May 20, 1856. ⁶⁹ On November 30, 1855, Charles delivered another paper on the Scheutz machine to the Royal Society, regretting that it had not been nominated for one of their medals, and suggesting that the lapse be remedied the following year. ⁷⁰

On August 29, 1855, the Scheutz machine was sent to Paris to be displayed in the Great Exposition of 1855, where it was accompanied and demonstrated by Gravatt. ⁷¹ The diagrams explaining it made by Henry Babbage in the mechanical notation were later sent to join the machine; the machine was eventually awarded the highest prize of the Exposition, a Gold Medal.

After the Exposition, the Scheutz machine was moved to the Imperial Observatory of Paris by order of the Emperor Napoleon III; ⁷² there was some confusion about this, for at first Babbage was under the impression that the French government had purchased the machine, and he suggested that they should also make Georg Scheutz a member of the Legion of Honor. ⁷³ In fact they had not purchased it, but asked the opinion of LeVerrier as to whether they should purchase it, and he recommended against this despite the fact that some other French scientists defended the machine, the government agreed. ⁷⁴

Either through publicity from the Paris Exposition or from direct communication with Babbage, with whom he corresponded, ⁷⁵ Benjamin Gould, director of the recently formed Dudley Observatory in Albany, New York, heard about the Scheutz Difference Engine, and on April 28, 1856, he wrote to Babbage asking about the powers of the machine, and requesting "information of the Yankee-est but of practical kind; is it for sale, and if so at what price?" ⁷⁶ Independently, the United States Nautical Almanac office sent similar enquiries to Edvard Scheutz on June 15, 1856. ⁷⁷

Babbage, however, still hoped to keep the Scheutz machine on the eastern side of the Atlantic. On June 23, 1856, Babbage wrote a letter - probably-to the French astronomer Claude Louis Mathieu - suggesting that even if the French did not want to buy the Scheutz machine for practical work at the Imperial Observatory, "it might yet be worth of a prominent place in any collection of Machines for performing intellectual calculations." Babbage said that such a collection would also have to include an original Pascal calculator and a Jacquard loom, the latter being important because "all my experience in contriving the Analytical Engine leads me to believe that those cards upon which I have engrafted a new principle will always form the simplest and most powerful means of conveying the commands of the human mind to automatic machinery." ⁷⁸

However, this plan did not work out, and later in the year arrangements were complete to sell the machine to the Dudley Observatory through Gould for the price of £1000. In a letter to Edvard Scheutz arranging the details of the transaction, dated December 22, 1856, Gould said:

What its fruits on this side of the Atlantic may be of course can not yet be anticipated; but I will trust that they may be such as to insure the absence of any regrets on your part that the product of your constant and toilsome labours for so many years should find its home in the western world. ⁷⁹

Gould suggested that among the uses to which the machine might be put were the computation of ephemerides and of the Nautical Almanac. He also requested that any report of the sale made in England should mention that the machine was a gift to the observatory in Albany from "an enlightened and public spirited merchant of that City, John F. Rathbone, Esq."

Before this sale had been arranged, however, the machine had been brought back from France to England in July, 1856. ⁸⁰ Apparently this was done (apart from the failure to sell the machine in France) in order to carry out a suggestion from Gravatt that "an endeavour should be made to obtain an acknowledgement of the practical usefulness of the invention by the publication of a collection of specimens of numerical Tables computed and printed by the machine," ⁸¹ The machine was installed in Gravatt's house, and the work was executed by him and Edvard Scheutz, in consultation with Babbage. The first sample pages of specimen tables calculated by the machine were sent by Gravatt to Babbage on October 18, 1856. ⁸² When finished, in about April, 1857, ⁸³ the booklet contained nearly forty pages of tables, the bulk of them comprising a complete table of logarithms, samples of other kinds of tables forming the remainder. The Scheutzes wrote a long preface to the work recounting the difficulties they had encountered along the way, and they dedicated the volume to Babbage, whom they called "one of the benefactors of mankind, and one among the noblest and most ingenious of the sons of England." ⁸⁴ Earlier, in February, 1856, the Scheutzes had expressed their gratitude for Babbage's help more personally in individual, formal letters of thanks; ⁸⁵ they had remarked there that his generosity was all the more remarkable since it might have been expected that he would feel some resentment toward them for having taken over what was clearly his idea.

During this same period, in a passage struck out from the letter to Mathieu cited above, written June 23, 1856, Babbage expressed his disinterest in resuming work on his own machines, and a firm conviction that the Analytical Engine "will never exist during my life." ⁸⁶ Some of his friends, however, wished that he would take up his work again. On July 28, 1857, I. K. Brunel, the noted engineer and a long time friend of Babbage, wrote him, saying: "Your name will ever be associated with the calculating machine, and the day will yet come (perhaps in your lifetime and mine) when your own comprehensive plans may be carried out; and this possibility might almost become a probability if the stone were once set rolling again." To set the stone rolling Brunel suggested that they raise money to build a second Scheutz machine, perhaps an improved model: "once set the system going and fresh wants would arise," perhaps ultimately leading to demand for an Analytical Engine. ⁸⁷

Through exactly what process the construction of the second Scheutz Difference Engine, as proposed by Brunel, was arranged is not clear, but principally two main facts converged to make it possible. First, Edvard Scheutz arranged with the engineering firm of Bryan Donkin to jointly offer to construct another model of the engine for £1200. ⁸⁸ Second, the General Register Office had accumulated a mass of data from the censuses of 1841 and 1851, and the registrations of births and deaths from 1838 to 1854, and wished to use this data in computing and publishing a new set of Life Tables, primarily under the impetus of William Farr. The Registrar-General, with the concurrence of the Astronomer Royal, Sir George Airy, ⁸⁹ recommended to the Home Department that the government acquire a Difference Engine for this work, so a contract was entered into with Donkin & Co., in about November, 1857, to build a new Scheutz machine. ⁹⁰ The machine was built by Donkin's firm, basically unchanged from the original Scheutz version, and was finished toward the middle of 1859. Upon completion, the machine was set to work in the General Register Office in the preparation of the English Life Table, which was issued in 1864. It is difficult to tell just how the machine was used, but it seems that to a certain extent it was set to duplicate certain tables which had been calculated by hand so that the two sets could be compared and verified., In the published version, less than one quarter of the tables were printed from plates stereotyped by the machine. ⁹²

The use of the English Scheutz machine was a source of some friction between Babbage and the Registry Office; Babbage felt strongly that it ought to have been exhibited at the British Exhibition of 1862, as an example of both calculating machinery and of the excellence of English workmanship; Babbage even had some scheme for exhibiting it alongside his own partial Difference Engine, having them both turned at slow rate by the same prime mover. The Registrar-General, however, felt that the use of the Scheutz machines in computing the Life Table was too important to be interrupted, and that the Scheutz machine was too delicate to be moved safely. Babbage eventually got quite angry at this and at the ill treatment he thought was shown toward his own machine when it was displayed at the Exhibition. ⁹³

After the publication of the English Life Table it does not appear that the English Scheutz machine was further used, and although some modifications were made to make the original machine, at this point in Albany, work better, it apparently was put to no significant use. ⁹⁴ For a few years the Scheutzes had continued trying to sell other copies of their machine, in the hope of finally making some profit from their years of work, but by 1861 this hope was abandoned, and Edvard Scheutz turned his attention to the invention of a new kind of rotary steam engine. ⁹⁵ The two Scheutz Difference Engines were in the long run deposited respectively in the Smithsonian Institution and in the Science Museum in South Kensington. Similarly, after being displayed at the International Exhibition of 1862, the Babbage Difference Engine was transferred to the South Kensington Museum, newly formed at that time; despite Babbage's belief that the machine would not be properly understood there, and that it should go to Cambridge University, it has remained in South Kensington ever since. ⁹⁶

Brunel's suggestion, in July, 1857, that promotion of the Scheutz Difference Engine would re-kindle interest in the Analytical Engine in the world at large, proved to be false. However, starting the previous month, Babbage's own interest had already been re-awakened, and he set to work on the Analytical Engine once again. He worked fairly steadily through the middle of 1859, and then abruptly stopped, doing almost nothing until February, 1863, when, as suddenly and unexplainably, he took the work up again, continuing it on and off from then until shortly before his death, on October 18, 1871.

Unfortunately, the character of Babbage's work during this period was much the same as that which he had done during the 1840s; ⁹⁷ that is, it led to no coherent, final, definite plans for the Analytical Engine, and was often concerned with re-thinking some notion previously rejected, or changing the character of the machine he was trying to design. In the case of the earlier period, this had been quite understandable, since Babbage had had no intention of trying to construct the Analytical Engine, and thus was not obliged to try to come up with final working plans. But in the period after 1857, the contrary was true; either seeing the Scheutz machine completed and working, or the improvements in the art of machining that had taken place, or some other reason had convinced Babbage that he could and should build the Analytical Engine in a few years.

Rather the reasons for the indecisive nature of Babbage's work near the end of his life were temperamental and temporal. The temperamental reason was his inability to leave something unchanged when he could think of an improvement; this was characteristic of him throughout life, and indeed if it had not been, he would never have invented the Analytical Engine in the first place. The temporal reason was that Babbage was getting old; in December, 1862 he was already seventy years old, and while his mind was still perfectly clear, he seemed to be no longer very able to carry out a course of development of his ideas over a long period of time. This is also testified to by Lionel Tollemache, who met Babbage first in the fall of 1861, and later wrote: "Ever since I first knew him, though he still retained much power of thought, he had lost the faculty of arranging his ideas, and of recalling them at will." ⁹⁸

An anecdote illustrative of Babbage's temperamental difficulty in constructing his machine was related by Lord Moulton in 1914. He visited Babbage a few years before he died, and was taken on a tour of the work-rooms. In the first room were parts of the Difference Engine, and Babbage explained that it was abandoned when the Analytical Engine was invented. In the second room were some parts from one version of the Analytical Engine; Moulton asked Babbage if he could see the whole machine;

"I have never completed it", he said, "because I hit upon an idea of doing the same thing by a different and far more effective method, and this rendered it useless to proceed on the old lines." Then we went into a third room. There lay scattered bits of mechanism, but I saw no trace of any working machine. Very cautiously I approached the subject, and received the dreaded answer, "It is not constructed yet, but I am working at it, and it will take less time to construct it altogether then it would have taken to complete . . . [the earlier version] from the stage in which I left it." ⁹⁹

A far larger amount of time was spent planning and considering the alternative forms of carriage; whole or half zero, hoarding or anticipating. On all too many occasions, Babbage would make a firm decision to adopt one kind of mechanism, and within a short time be considering the alternate possibility all over again. ¹¹⁰ Further, Babbage's reasoning tended to shift its ground. Thus he would often argue for some more complicated mechanism, because it would save time (as half zero carriage); generally he would argue for a simpler mechanism on the grounds that its simplicity was worth the sacrifice of a small amount of time; ¹¹¹ but sometimes he would argue that the machine was faster than needed anyway, ¹¹² or even that the simpler form would turn out to be faster. ¹¹³ All these same kinds of arguments also went into the question of whether the machine should do multiplication and division with or without table.

For all these reasons, it would not be profitable to survey in any detail here the multitude of forms through which Babbage's plans for the Analytical Engine fluctuated and varied during this last phase of his life. Rather, the brief account here will focus primarily on his external communications concerning the Engine, principally in his correspondence, but naturally in the context of the work he was actually doing.

As was said above, Babbage's interest in the Analytical Engine was revived in June, 1857, ¹¹⁴ and in contrast to the period of his earlier work on the machine, he now intended actually to construct it. He immediately set about making drawings both of new general plans and of new forms of the detailed mechanisms; he also worked at designing various complex machine tools to use in the construction. By March, 1858, he had settled on what was to remain his ideal size for a full scale machine, namely one which could handle 1000 variables of fifty digits per variable, where each column was to be about sixty inches high. ¹¹⁵ In July through November, 1858, Babbage corresponded extensively with Joseph Whitworth in Manchester, ordering from his factory various tools and parts he would need. ¹¹⁶

He became concerned, however, that the machine would be too physically large to be easily constructed; in September, 1858, he conducted experiments with various alloys out of which to cast his gears; he found one whose strength satisfied him that he could reduce the size of the parts of the machine by one half, reducing the axes to thirty inches, and thus making even the necessary tools easier to build. ¹¹⁷ Later he was to compromise and further reduce the size of the Engine by reducing the number of variables, as mentioned above.

The primary change in the overall design of the Analytical Engine during this period was the abandonment of the original plan of Mill axes arranged around large central wheels with the Store extending linearly out one side along a set of racks, in favor of a plan where Mill and Store were both arranged rectangularly, with several sets of racks at right angles to one another and having the power to communicate between themselves, and thus between any different axes. This rectangular design took many forms, sometimes having the Mill and Store separate, and sometimes quite physically integrated, but the basic idea Babbage stayed with for the rest of his life. ¹¹⁸ The greatest advantage of this was that it allowed the machine to be much more compact; a Store providing for 1000 variables could be as small as three feet on a side; ¹¹⁹ it was also much easier to construct linear racks than immense central gears.

The progress he made gave Babbage the confidence to predict, in March, 1859, that he would complete the Analytical Engine "in two or at most three years." ¹²⁰ Yet for unknown reasons, in September, 1859, Babbage's work on plans for the machine abruptly ceased, and was not resumed in any substantial way until January, 1861; ¹²¹ as far as one can tell, all work on construction ceased also, though why the work was suspended is not at all clear. It was resumed again in the period from January to March, 1861, ¹²² but then dropped again until February, 1863. ¹²³

One suggestion that Babbage did not take up during this hiatus in the work was sent to him by William Gravatt, in a letter dated February 3, 1860. Gravatt said that he had heard of the invention by an Italian of "a machine for Weaving by Electro-Magnetism." Strips or sheets of gutta-percha were to be gilded or covered with tin foil; the metallic surfaces were to be painted in various patters with a non-conducting pigment; then a loom could be controlled by the particular pattern of electrical flow set up when needles were pressed against the cards, in a manner analogous to that in the Jacquard loom. Gravatt said that he had not seen the machine and did not understand the details of it, but that the principle might be applicable to the Analytical Engine. ¹²⁴ In any case, Babbage did not choose to follow this suggestion up.

The causes which made Babbage take up the Analytical Engine for a few months in 1861 are not clear, but at least one factor instrumental in his return to it in February, 1863 can be pointed out. This was the encouragement of the Countess Teleki, who was perhaps the most prolific of Babbage's correspondents during the 1860s. The daughter of Henry Bickersteth, Lord Langdale, she married Count Alexander Teleki. ¹²⁵ Although she doubtless did not understand the principles of the Analytical Engine as well as had Lady Lovelace, it is clear from her letters that she understood Babbage much better.

The first important letter from her to Babbage was dated October 3, 1862. Apparently she had recently been learning about the Analytical Engine, and was distressed at Babbage's intention to have no more to do with it. She wrote:

The more I think of it, the more I am distressed at your thinking it possible that you should give up the Analytical Engine. To strangle an idea and a great invention after so much pains to bring it to perfection, appears to me a kind of moral murder, and an injury to the whole human race, which it cannot be right to inflict . . . It is certain that you, and you only, are capable of completing the Analytical [Engine], which if you abandon it, must perhaps remain unrealized for ages, and great tho' it be to conceive an idea hundreds of years in advance of one's kind, it surely is greater, by realizing that idea, to make the human race, in one generation, outstrip the progress of many. ¹²⁶

In February, 1863, the Countess was preparing for a trip to Italy, including a long visit to Turin, and Babbage wrote her a letter of introduction to General Menabrea. Although Babbage had by this time resumed work on the Analytical Engine, he said of it in this letter only: "Circumstances have not favored its completion. I hope however if I live five or six years more I may yet see it at work." ¹²⁸

On March 12, 1863, in reply to a now missing letter from Babbage, Countess Teleki wrote:

I was indeed somewhat surprised to hear of the immense change you have introduced into the construction of the engine, tho my chief feeling about it is pleasure at the great progress you seem to have made lately, and at the hope of completing the machine which you derive from its increased simplicity and diminished expense. ¹²⁹

This enthusiasm was to continue. On August 6, 1863, Babbage wrote to John Henry Alexander in Baltimore, saying that he had:

succeeded in simplifying its structure beyond any expectation I formerly had. As far as my drawings and carefully made models of many parts go, I have no doubt in a few years I shall succeed in placing all the developments of Analysis under the dominion of mechanism; and also be able to execute all the most extensive processes of arithmetic in an unexpectedly short time.

I have not the slightest hesitation in expressing my perfect confidence that when the Engine itself is set to work it will be able to multiply any two numbers of fifty figures each and print the product of one hundred in less than one minute of time. The inverse operation of division may be accomplished to the same extent in an equally short time. ¹³⁰

What you tell me of your machine is perfectly marvelous; 50 figures by 50 figures in one minute seems almost to surpass the velocity of thought. In old times you certainly would have risked being burned as a witch. ¹³¹

I am very glad to hear your progress has been so satisfactory, and I hope that as you have now arrived at the ultima Thule of simplicity you will now really make the engine without searching for further improvements. Don't forget the proverb I have so often already quoted to you: Le Mieux est l'ennemi du bien. ¹³²

Countess Teleki expanded on these suggestions in her next letter, dated December 10, 1863:

I am delighted to hear that you are satisfied at last with the mechanism of the new carriage, and that you will not seek a better, for with your ingenuity, I am always afraid of some fresh idea striking you as likely to be an improvement, and of your setting to work in consequence on another set of drawings, instead of constructing the Engine itself; but this time I do hope you will be satisfied, since the carriage, which is the soul of the whole, is ready to do its work with all desirable speed and simplicity. ¹³⁵

In this same letter, the Countess commented at length on proofs Babbage had sent her of Chapter XXII of Passages from the Life of a Philosopher, which was a sketch entitled "Scenes from a New Afterpiece," satirizing Babbage's unsuccessful venture into politics in 1832. She said that while it was very amusing, those not acquainted with Babbage's true character might be misled by the self-caricature he provided in the play. ¹³⁷

The next letter of special interest was one discussing intended applications of the Analytical Engine, written by Babbage to the Emperor Louis Napoleon on November 16, 1864, accompanying a gift copy of Passages from the Life of a Philosopher, which had finally been published earlier in the summer. Babbage wrote:

The Analytical Engine, which has occupied me during the greater part of my life, is now so far simplified that I may reasonably expect, if I live some few years longer, to complete it and make it productive of extensive computations . . . .

The first task ... . which I shall propose for the Analytical Engine will be to recalculate the whole of the table of Natural Sines to every 10,000th part of the quadrant.

This however will be but a trifling exertion of its powers. In the earliest period of its existance it ought to be employed in recomputing the formulae and in verifying the coefficients of Laplace in his investigations of the problem of the three bodies. After that it might be used to develop the still more complicated problem of the three bodies when they are acting under the conditions that each is a magnet with several poles and that the transmission of magnetism unlike that of gravity is not instantaneous. ¹³⁸

This day I finally ??? (I hope) resolved to give up the mechanism for shortening by a very short time the operation of Multiplication, and to confine the Analytical Engine to its own great laws of developing the science which it embodies in is mechanism. ¹³⁹

In March, 1871, Henry P. Babbage reached England on a second furlough from his duties in India. In contrast to his furlough in 1854-56, however, on this occasion he did not become involved in his father's work, spending most of his time with his wife and children in a rented house in Bromley, visiting Charles only occasionally. However, when Charles became seriously ill in early October, 1871, Henry moved in with him to manage his affairs. A new will was signed on the 13th, leaving all effects connected with the calculating machines to Henry. After a painful illness, Charles died on October 18, 1871. He was buried six days later in Kensal Green Cemetery. ¹⁴⁸

The attempted construction was carried on by Henry P. Babbage, who, as mentioned above, had been left all the material relating to the calculating machines belonging to his father. This included a number of parts which had been left unassembled when the construction of the Difference Engine No. 1 was abandoned; a large number of them had been sold to Babbage by the government for their value as scrap metal; ¹⁴⁹ subsequently, much of the metal was melted down for use in the Analytical Engine. However, enough of the original parts were left for Henry to assemble some six small sections intended to demonstrate the mechanical action of the Difference Engine, and he sent some of these to different Universities for their collections. ¹⁵⁰ He also inherited a number of parts for the Analytical Engine and tools intended for its construction. On March 1, 1872, Henry sold most of these, but he kept three lathes and some other tools; ¹⁵¹ he also retained the workman, Wright, who had been employed by his father, for he had already decided to try to complete the Mill, ¹⁵² and had been working sporadically on the carriage mechanism and other parts since his father's death. ¹⁵³ In March through August, 1872, work was continued on constructing and assembling the necessary pieces for making part of the Mill. Two adding columns and one carriage column, and most of the printing apparatus, together with the connecting racks, were completed, but the directive and driving apparatus, especially the card reading apparatus, were not made, so the section put together could not function even as a demonstration piece. It is quite hard to tell, but it seems that perhaps about half of the parts of this section of the Analytical Engine (now in the South Kensington Museum) were completed before Charles' death. ¹⁵⁴

In July, 1872, Henry had construction started on a workshop on some land he had purchased in Bromley, where he also was building a home for his family. In September, the house in Dorset Street in which his father had lived for over forty years was sold, and the tools and machinery were moved to the new workshop. Yet although Henry did not return to service in India for over a year, partly due to ill health, it seems that no further work on the machine was done. ¹⁵⁵

After his retirement from the Army, Henry Babbage returned to live in England. He worked sporadically on a new version of part of the Mill of the Analytical Engine, and with the engineering firm of W.B. Monroe, finished construction in 1910. The only work it was set to do was to construct a table of the first twenty two multiples of pi, expressed to twenty eight places, and this was printed up for exhibit. Despite the fact that this was an elementary problem in addition, it was found that there were several mistakes in it. ¹⁵⁶ The failure of this model to amount to much was no doubt in part due to the fact that Henry Babbage by this point was eighty six years old.

Knowledge of the machine by the world at large was a similar case of interest shown without bearing fruit. One of the earliest and most interesting expressions of confidence in the future importance of the Analytical Engine came from William Farr, who earlier had used the Scheutz machine in preparing the English Life Tables, and was now President of the Statistical Society of London (later the Royal Statistical Society), of which Babbage had been the principal founder. In an address to the Society on November 21, 1871, Farr included some extensive memorial remarks on Babbage, including the following:

I feel persuaded that ere many years an analytical machine will be at work, calculating accurately not only those elaborate numerical coefficients of the moon which puzzle the greatest adepts, but those still more complicated coefficients and variables which, it is easy to foresee, will be in requisition when future State problems are dealt with scientifically by a political Newton. ¹⁵⁷

Later the same year it seems that the extant portion of Babbage's Difference Engine No. 1 was given more prominent display among the Science Collections for Teaching and Research of the Victoria and Albert Museum in South Kensington, for in September, 1872, B. Herschel Babbage, another of Charles' sons, wrote up a manual on the machine, including instructions to the operator, which was published by the Museum. ¹⁶⁰

Clifford's interest in the Analytical Engine continued, for he was largely responsible for the formation of a committee of the British Association for the Advancement of Science, "appointed to consider the advisability and to estimate the expense of constructing Mr. Babbage's Analytical Machine." ¹⁶¹ They considered the published papers on the Analytical Engine, and inspected the drawings, parts and notes which Babbage had left behind, and reported their conclusions to the 1878 meeting of the British Association.

As to the theoretical significance of the Analytical Engine as a potential practical machine, they had no doubts, though they issued also a most interesting and far-sighted warning:

If intelligently directed and saved from wasteful use, such a machine might mark an era in the history of computation, as decided as the introduction of logarithms in the seventeenth century did in trigonometrical and astronomical arithmetic. Care might be required to guard against misuse, especially against the imposition of Sisyphean tasks upon it by influential sciolists. This, however, is no more than happened in the history of logarithms. Much work has been done with them which could more easily have been done without them . . . Yet, on the whole, there can be no reasonable doubt that the first calculation of logarithmic tables was an expenditure of capital which has repaid itself over and over again. So probably would the analytical engine, whatever its cost, if we could be assured of its success. ¹⁶²

Ten years after this report was issued, Henry P. Babbage himself read a paper to the British Association in which he commented on and to some extent rebutted the committee's opinion, and announced the forthcoming publication of Babbage's Calculating Engines; he also gave a clear, though limited, description of the mechanical principles and operation of the Analytical Engine. He took issue with the earlier report as to the amount of difficulty there would be in transforming the plans Babbage had left behind into working drawings. However, Henry added that he did not see that construction of the Engine would be profitable, and he did not intend to undertake it himself: "The History of Babbage's Calculating Machines is sufficient to damp the ardour of a dozen enthusiasts." ¹⁶⁵ Those who wished to see the machine constructed, he suggested, would do best to show that it could be profitable in some way. ¹⁶⁶

Apart from the work done by Henry Babbage at the very end of his life, discussed above, this was essentially the last serious notice taken of the Analytical Engine by those who had in some way been more or less contemporary with it. And although the name of Charles Babbage continued to be remembered, it was more likely to be for his eccentricities than for the invention of the Analytical Engine.

The calculating machines were not forgotten by all, however; on the occasion of the Napier Tercentenary Exhibition in 1924 in Edinburgh, F.J.W. Whipple made the following remarks:

In these days of automatic tools, Babbage's [Difference] Engine could be constructed at a moderate cost . . . . The story of Babbage's efforts end [sic] at present in a confession of national failure, and it would be gratifying to British mathematicians if a happier sequel could be written in our annals. ¹⁶⁷

What was evidently a more prevalent view was expressed shortly after this in the article on Babbage in the Dictionary of National Biography, where it was said of the Analytical Engine: "This extraordinary monument of inventive genius . . . remains, and will doubtless forever remain, a 'theoretical possibility.'" ¹⁶⁹

By the 1930s, the use of difference machines in scientific computation had become fairly common, and Babbage began to be remembered as the inventor of the Difference Engine, rather than for the Analytical Engine. This is well illustrated by a paper read at the Science Museum, in South Kensington on December 13, 1933, by L.H. Dudley Buxton, grandson of H. Wilmot Buxton, Babbage's friend and biographer. The paper and the subsequent discussion (entered by, among others, L.J. Comrie) dwelt on the Difference Engine at great length, almost totally ignoring the Analytical Engine. ¹⁷⁰

It was only four years later that Howard Aiken of Harvard wrote the "Prospectus" for the computer known as Mark I, which was finished in 1944, and is now often considered to have been the first operating general purpose automatic digital computer. Mark I and its successors will not be discussed here, but it must be noted that in the 1937 "Prospectus," Aiken described the Difference and Analytical Engines at some length in an historical introduction. ¹⁷¹ Where Aiken had learned about Babbage, ¹⁷² how much he knew about the Analytical Engine, ¹⁷³ or whether he learned about it before or after he developed his own ideas for a computing machine, is not known.

Babbage's invention of the Analytical Engine was also discussed at length in the first volume of the Annals of the Computational Laboratory of Harvard University, ¹⁷⁴ which was devoted primarily to Mark I. The historical introduction quoted extensively from Babbage's Passages from the Life of a Philosopher, and also concluded that Babbage's failure to complete either the Difference or Analytical Engines "was not due to a lack of understanding of the principles and purposes of the engines that he designed, but rather to his lack of machine tools, materials of construction and electrical circuits." ¹⁷⁵

The degree to which Babbage was immediately recognized as the true forerunner of the computer is also indicated by the fact that the review of this same volume of the Annals in Nature carried the title "Babbage's Dream Comes True." ¹⁷⁶

We may close by noting that the long period which elapsed after Babbage's death before computers were actually constructed, and the degree to which, after that, he was given credit for the invention, would have been no surprise to him. Writing in 1864 of the construction of the Analytical Engine, he had said:

Half a century may probably elapse before anyone without those aids which I leave behind me will attempt so unpromising a task. If, unwarned by my example, any man shall undertake and shall succeed in really constructing an engine embodying in itself the whole of the executive department of mathematical analysis upon different principles or by simpler mechanical means, I have no fear of leaving my reputation in his charge, for he alone will be fully able to appreciate the nature of my efforts and the value of their results. ¹⁷⁷

FOOTNOTES

#1 Jonathan Swift, Gulliver's Travels (Penguin, London, 1967). PP. 70-71.

#2 As: S.B., Vol. II, p. 226, November 19, 1836; S.B., Vol. V, p. 80, late 1841, and p. 460, November 11, 1843; also S.K., Drawing II, 99, April and May, 1842.

#3 S.B., Vol. VI, p. 97.

#4 P.L.P., p. 97.

#5 P. 177.

#6 B.M., Vol. XII, ff. 347-57.

#7 B.S., Vol. XII, f. 357.

#8 S.B., Vol. VI, p. 105.

#9 See note on B.M., Vol. XII, f. 349.

#10 B.M., Vol. XIII, f. 337.

#11 S.K, Notation 385, Drawing II, 178 Sheet 1; the confusion in the numbering of the drawings of the Difference Engine No. 2 will be discussed in the Bibliography.

#12 S.K., Notation 385; S.B. Vol. VI, passim.

#13 B.M., Vol. XIII, f. 253; this letter is addressed to "Hayward."

#14 S.B., Vol, VI, p. 301.

#15 S.B., Vol. VI, pp. 267, 293; B.M., Vol. XIII, f. 266.

#16 P.L.P., p. 105.

#17 P.L.P., p. 104.

#18 The Earl of Rosse (William Parsons), President of the Royal Society, in an address to the Society on November 30, 1854; Proc. Roy. Soc., Vol. VII, (1854-55), p. 257. Doubtless Rosse was echoing Babbage's views.

#19 From a letter from Babbage to Lord Derby, June 8, 1852; B.M., Vol. XIV, ff. 80-83, reprinted in P.L.P. pp. 100-107.

#20 B.M., Vol. XIV, ff. 72-73.

#21 P.L.P., pp. 104-5.

#22 P.L.P., p. 100; B.M., Vol. XIV, ff. 108-9, 127-32.

#23 P.L.P., p. 107.

#24 B.M., Vol. XIII, f. 336 (though wrongly placed by the cataloguer).

#25 Proceedings of the Royal Society, Vol. VII (1854-55), p. 257.

#26 B.M., Vol. XIV, ff. 108-9.

#27 B.M., Vol. XIV, f. 113.

#28 See, e.g., G.S.B., 1. 4881-4942, 5751; S.K. Travelling Scribbling Book, pp. 186-87.

#29 S.B., Vol. X, p. 394.

#30 P.L.P., pp. 465-71.

#31 B.M., Vol. XIV, f. 118.

#32 B.M., Vol. XIV, ff. 119-20.

#33 B.M., Vol. XIV, ff. 123-26.

#34 P.L.P., p. 109.

#35 P.L.P., pp. 110-111.

#36 P.L.P., p. 111.

#37 B.M., Vol. XIV, ff. 127-32.

#38 As shown in B.M., Vol. XIV, ff. 108-9.

#39 B.M. Vol. XIV, ff. 130-31.

#40 Proc. Roy. Soc., Vol: VII (1854-55).p. 255.

#41 B.M., Vol. XV, ff. 251, 255.

#42 B.M., Vol. XV, ff. 266-67.

#43 B.M., Vol. XV, ff. 257-58.

#44 B.M., Vol. XV, f. 251.

#45 The Exposition of 1851 (London, 1851), p. 176.

#46 B.M., Vol. XVIII, f. 499.

#47 Samuel Smiles, Industrial Biography: Iron-workers and Toolmakers (Boston, 1864 , p. 298; Chapter XIII of this invaluable book is much the best source of information on Clement.

#48 Vol. XXXVI (1818), pp. 133-77; Vol. XLIII (1825), pp. 138-42; Vol XLVI (1828), pp. 67-105; Vol. XLVII (1829), pp. 131-35; Vol. XLIX (1832), pp. 157-85.

#49 See Smiles, Industrial Biography, pp. 302-3; B.M., Vol. XV, ff. 264-65.

#50 Smiles, Industrial Biography, pp. 306,313.

#51 P. 304.

#52 Smiles, Industrial Biography, P. 313.

#53 B.M., Vol. XV, ff. 264-65; see also Transactions of the Society of Arts, Vol. XLIX (1832), p. 157.

#54 Discussed in Chapter Two.

#55 Proceedings of the Institution of Mechanical Engineers for 1856, pp. 125-33.

#56 For biographical details, see; Biographiskt Lexicon öfver Namnkunnige Svenka Män (Upsala, 1847), Vol. XIV, pp. 54-66; and Svenskt Biografiskt Handlexikon (Stockholm, 1906), Vol. II, pp. 428-29.

#57 See Chapter Two.

#58 B.C.E., p. 260.

#59 This and other material below without specific reference is from Specimen Tables Calculated and Stereomoulded by the Swedish Calculating Machine (London, 1857), pp, vi-xv.

#60 Apparently their publicity was not widespread, for certainly Babbage had not heard of the Scheutz machine until well into the 1850s.

#61 B.C.E., p. 261.

#62 B.C.E., p. 249.

#63 All the material here on the mechanical aspects of the Scheutz machine is based on personal inspection.

#64 British Patent 1854, No. 2216.

#65 B.C.E., pp. 264-69.

#66 B.M., Vol. XV, f. 253; cf. f. 304; and B.C.E., pp. 268-69.

#67 Memoirs and Correspondence of Major-General H.P. Babbage (London, 1910), p. 85.

#68 Report of the 25th Meeting of the B.A.A.S., (London, 1856) Part II, pp. 203-5; reprinted in B.C.E., pp. 246-47; the charts are now in the South Kensington collection.

#69 B.C.E., pp. 248-57.

#70 B.C.E., pp. 260-61.

#71 B.M., Vol. XV, ff. 302-3.

#72 B.C.E., p. 261.

#73 B.M., Vol. XV, f. 372.

#74 B.M., Vol. XVI, f. 336 (though the letter was written about August, 1856, and is misplaced); of Vol. XIII, ff. 403-4 (also misplaced).

#75 See, e.g., B.M., Vol. XIV, f. 547.

#76 B.M., Vol. XVI, ff. 483-86.

#77 B.M., Vol. XVI, f. 53.

#78 B.M., Vol. XIII, ff. 403-4 (the year is not specified, but is clear from the context, although the letter was badly misplaced by the cataloguer; that the addressee was Mathieu is also suggested by the context). Cf. B.M., Vol. XV, f. 372 and B.C.E., p. 261.

#79 B.M. Vol. XVI, ff. 136-37.

#80 B.M. Vol. XVI, f. 77.

#81 Specimen Tables, p. xiv.

#82 B.M. Vol. XVI, f. 108.

#83 B.C.E., p. 270.

#84 Specimen Tables, p. xv.

#85 B.M., Vol. XV, ff. 418-20.

#86 B.M., Vol. XIII, ff. 403-4.

#87 B.M., Vol. XVI, ff. 230-31.

#88 English Life Table (London, 1864), p. cxli. But H. Wilmot Buxton, in a letter to Babbage dated August 20, 1863 (B.M., Vol. XVII, ff. 540-41), said that the contract had been for £1000, and that the firm had lost an additional £200.

#89 In contrast with his recommendations concerning the Babbage Difference Engine No. 1 in 1842; see Chapter Two.

#90 English Life Table, p. cxli; B.M., Vol. XVI, f. 251; Journal of the Statistical Society, Vol. XXXIV (1871), p. 416.

#92 The machine calculated and stereotyped plates can be distinguished easily by their typography. In addition to the above two references, see English Life Table, esp. pp. xiii, cxxxix-cxlv; also Companion to the Almanac; or, Year-book of General Information for 1866 (London, 1866), pp. 6-15.

#93 For the two sides, see P.L.P., Chapter X, and English Life Table, pp. cxxix-cxl.

#94 But see the fine description of it in the Annals of the Dudley Observatory, Vol. I (1866), pp. 116-26. Further, there is some unpublished print-out from the Scheutz machine still at the Observatory.

#95 B.M., Vol. XVII, ff. 142-43, January 25, 1861.

#96 B.M., Vol. XVII, f. 467; Vol. XVIII, ff. 403-4.

#97 See Chapter Three.

#98 Lionel A. and Mrs. Tollemache, Safe Studies (London, 1884), p. 148.

#99 Napier Tercentenary Memorial Volume, ed. Cargill Gilston Knott (London, 1915), pp. 19-20.

#100 S.B., Vol. VI, p. 304.

#101 "Description of the Analytical Engine as at present proposed," in S.K., "Sundry Papers;" dated March 16, 1858.

#102 S.B., Vol. VII, p. 254.

#103 S.B., Vol. VIII, p. 207.

#104 S.B., Vol. VIII, p. 241.

#105 S.B., Vol. VIII, p. 253.

#106 S.B., Vol. IX, p. 500.

#107 S.B., Vol. X, p. 200.

#108 S.B., Vol. X, p. 217.

#109 S.B., Vol. XI, p. 345.

#110 As: S.B., Vol. X, p. 164 vs. pp. 205ff; also S.B., Vol. XII, p. 166 vs p. 139.

#111 As: S.B., Vol. XI, p. 95.

#112 As: S.B., Vol. IX, p. 13; S.B., Vol. X, p. 78.

#113 As: S.B., Vol. X, p. 17.

#114 S.B., Vol. VI, p. 304.

#115 "Description of the Analytical Engine as at present proposed," S.K., "Sundry Papers."

#116 B.M., Vol. XVI, ff. 324, 325, 354,373.

#117 S.B., Vol. VII, pp. 146-47.

#118 Although he considered switching back to central wheels as late as December, 1870; S.B., Vol. XII, p. 94.

#119 S.B., Vol. VII, p. 173.

#120 B.M., Vol. XVI, f. 406.

#121 S.B., Vol. VIII, pp. 72-74.

#122 S.B., Vol. VIII, pp. 74-130.

#123 First in Travelling Scribbling Book, pp. 188-97; then in S.B., Vol. VIII, pp. 131ff.

#124 B.M., Vol. XVI, ff. 489-90.

#125 See: Catalogue of Additions to the Manuscripts in the British Museum in the years 1900-1905 (London, 1907) pp. 491, 866. Contrary to what Moseley says in Irascible Genius (pp. 197, 241), her name was neither Countess Harley nor Countess Harley-Teleki.

#126 B.M., Vol. XVII, ff. 406-7.

#127 B.M., Vol. XVII, f. 405 (slightly misplaced).

#128 B.M., Vol. XVII, f. 494. It is clear from the letter that Countess Teleki did not know Menabrea before this date, and the things Moseley says (Irascible Genius, pp. 22, 197) about her being an "intermediary" between Babbage and Menabrea are nonsense.

#129 B.M., Vol. XVII, ff. 501-2.

#130 B.M., Vol. XVII, ff. 531-32.

#131 B.M., Vol. XVIII, ff. 1-2.

#132 B.M., Vol. XVII, f. 548.

#133 Quoted in: Transactions of the Newcomen Society, Vol. XIV (London, 1933), p. 50.

#134 B.M., Vol. XVIII, ff. 9-10.

#135 B.M., Vol. XVIII, ff. 13-14.

#136 B.M., Vol. XVIII, ff. 38-39.

#137 Moseley has quoted at length from these same remarks (Irascible Genius, pp. 241-42), but she has mistakenly taken then to apply to the whole book, not just the one chapter.

#138 B.M., Vol. XVIII, ff. 151-52.

#139 S.B., Vol. XI, pp. 45-46.

#140 P.L.P., p. 496.

#141 B.M., Vol. XVIII, f. 216.

#142 B.C.E., Preface.

#143 London, 1889.

#144 B.M., Vol. XVIII, ff. 477-78.

#145 The four major essays were "General Description of the Analytical Engine," May 4, 1869, S.B., Vol. XIA, pp. 134-36; and the following three from Buxton, Vol. VIII; "Of the Analytical Engine," July 19, 1869; "On the Analytical Engine," October 7, 1869; and "The Analytical Engine," November 8, 1869.

#146 See S.B., Vol. VIII, p. 148; S.K., Drawing 199; B.M., Vol. XVIII, f. 257.

#147 S.B., Vol. XII, p. 401.

#148 Memoirs and Correspondence of Major-General H.P. Babbage, pp. 178-82.

#149 See Chapter Two.

#150 B.C.E., p. 341. There are examples of these small models at Harvard University; at the Museum of the History of Science at Oxford University; and in the collection of IBM, in New York. Henry Babbage mentioned having sent others to Cambridge University and to Owens College, Manchester.

#151 S.B., Vol. XII, p. 181,

#152 B.M., Vol. XVIII, ff. 558-59.

#153 S.B., Vol. XII, pp. 158ff; that this is Henry Babbage's handwriting is confirmed on p. 163.

#154 On Henry's work, see: S.B., Vol. XII, pp. 182-88; cf. p. 401.

#155 Memoirs of H.P. Babbage, pp. 185-86.

#156 Memoirs of H.P. Babbage, pp. 227-28.

#157 Journal of the Statistical Society, Vol. XXXIV (1871), p. 415.

#158 Notices of the Proceedings of the Royal Institution, Vol. VI (1872), p. 533.

#159 Memoirs of H.P. Babbage, p. 184.

#160 "Babbage's Calculating Machine; or Difference Engine," London, 1872.

#161 Memoirs of H.P. Babbage, p. 184; B.C.E., p. 323. The committee report can be found in B.C.E., pp. 323-30. reprinted from: Report of the 48th Meeting of the B.A.A.S. (London, 1879), pp. 92-162.

#162 B.C.E., P. 329.

#163 B.C.E., P. 330.

#164 Ibid.

#165 B.C.E., p. 337.

#166 The paper is printed in full in B.C.E., pp. 331-37.

#167 Modern Instruments and Methods of Calculation, ed. E.M. Horsburgh (London, 1914), p. 75.

#168 Ibid., pp. 124-27.

#169 Agnes M. Clerke, "Charles Babbage," Dictionary of National Biography, Vol. I (Oxford, 1919), p. 778.

#170 Transactions of the Newcomen Society, Vol XIV (1833-34), pp. 43-65.

#171 The original draft copy of the "Prospectus" is in the Harvard University Archives.

#172 There was a copy of Babbage's Calculating Engines at Harvard.

#173 The fact that Mark I was in some respects a good deal more primitive than the Analytical Engine (as with its provisions for program branching) suggests that Aiken didn't know much about Babbage's plans.

#174 Vol. I, Cambridge, Mass., 1946.

#175 Annals, p. 7.

#176 Nature, October 26, 1946 (No. 158). pp. 567-68.

#177 P.L.P., p. 450. Babbage's rough estimate of fifty years before a computer would be built brought him to 1914; this was some ten to fifteen years before the construction of Mark I would have been feasible, but thirty years before it was actually finished.